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Extending echo state property for quantum reservoir computing

5 March 2024
Shumpei Kobayashi
Quoc Hoan Tran
Kohei Nakajima
ArXiv (abs)PDFHTML
Abstract

The echo state property (ESP) represents a fundamental concept in the reservoir computing (RC) framework that ensures output-only training of reservoir networks by being agnostic to the initial states and far past inputs. However, the traditional definition of ESP does not describe possible non-stationary systems in which statistical properties evolve. To address this issue, we introduce two new categories of ESP: non-stationary ESP\textit{non-stationary ESP}non-stationary ESP, designed for potentially non-stationary systems, and subspace/subset ESP\textit{subspace/subset ESP}subspace/subset ESP, designed for systems whose subsystems have ESP. Following the definitions, we numerically demonstrate the correspondence between non-stationary ESP in the quantum reservoir computer (QRC) framework with typical Hamiltonian dynamics and input encoding methods using non-linear autoregressive moving-average (NARMA) tasks. We also confirm the correspondence by computing linear/non-linear memory capacities that quantify input-dependent components within reservoir states. Our study presents a new understanding of the practical design of QRC and other possibly non-stationary RC systems in which non-stationary systems and subsystems are exploited.

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